Question

A piece of metal weigh 46 g in air.When it is immersed in a liquid of specific gravity 1.24 at 270 c ,it weigh 30 g.When the temp is raised to 42o c ,the metal piece weigh 30.5 g.If the specific gravity of liquid at 420 c is 1.2 ,then coefficient of linear expansion of metal is

Answer 1

Answer:

The coefficient of linear expansion of metal is $2.41\times10^{5}\ ^{\circ}C^{-1}$

Explanation:

Given that,

At 27° C,

Loss in the mass of the metal =mass of liquid displaced =46-30 = 16 g

Volume of metal at 27° C= Volume of liquid displaced at 27° C

At 42° C,

Loss in the mass of the metal =mass of liquid displaced =46-30.5 =15.5 g

Volume of metal at 42° C= Volume of liquid displaced at 42° C

The volume of the metal at 27° C is

$V=\dfrac{mass\ of\ liquid\ displaced }{density\ of\ liquid}$

$V=\dfrac{16}{1.24}$

$V=12.903\ cm^3$

The volume of the metal at 42° C is

$V'=\dfrac{46-30.5}{1.2}$

$V'=12.917\ cm^3$

Coefficient of cubical expansion of metal is

$\gamma=\dfrac{V'-V}{V(T_{2}-T_{1})}$

$\gamma=\dfrac{12.917-12.903}{12.903(42-27)}$

$\gamma=7.23\times10^{5}\ ^{\circ}C^{-1}$

Since, $\gamma=3\alpha$

$\alpha=\dfrac{\gamma}{3}$.....(I)

The coefficient of linear expansion of metal is

Put the value of gamma in equation (I)

$\alpha=\dfrac{7.23\times10^{5}}{3}$

$\alpha=2.41\times10^{5}\ ^{\circ}C^{-1}$

Hence, The coefficient of linear expansion of metal is $2.41\times10^{5}\ ^{\circ}C^{-1}$